At his United Nations debut, Barack Obama urged global cooperation to combat nuclear proliferation, climate change and other problems that go beyond the borders of any one country. The speech was well received around the world, except in one place -- America's right-wing netherworld, which quickly began whipping people into a frenzy. For Michelle Malkin, the speech was evidence that Obama was "the great appeaser," though she went on to say, "From the sound of it, you'd think you were listening to Thomas Jefferson." (That's bad?) For Rush Limbaugh, Obama's speech was "basically a coup against America." At the National Review's Web site, a debate -- an entirely serious debate among serious people -- broke out as to whether the speech proved that Obama actually wanted the world's tyrants to win, in the tradition of past intellectuals who admired Mussolini and Hitler. This is the discourse of American conservatism today: Obama is bad because he loves "death panels" and Hitler.

There is a serious case to be made that it's not worth taking the United Nations seriously, that it's an anachronistic institution based on 60-year-old geopolitics and a platform for tyrants and weirdos. But while much of that is true, the United Nations is the only organization in the world to which all countries belong. As such it does have considerable legitimacy. And that means power. As David Bosco points out in Foreign Policy magazine, over the past two decades the Security Council has authorized "more than a dozen peacekeeping missions, imposed sanctions or arms embargoes on 10 states, and created several war crimes tribunals to prosecute those responsible for genocide and crimes against humanity, including sitting heads of state." It's worth putting in the effort to shape its decisions.

Obama's speech was part of a calculated strategy. In sentiment it recalls Richard Nixon's line after losing the California governor's race in 1962: "You won't have Nixon to kick around anymore." Obama was telling the world: The United States is willing to be cooperative, to rejoin international institutions, to adhere to treaties. But in return, other countries will have to help solve some of the world's common problems. You can't just kick us around anymore.

Let's go back one year. Many countries had come to believe that America showed little interest in the world. This hostility had become an easy excuse to reject even modest concessions to U.S. requests. If this sounds partisan, recall that after he was elected president of France in 2007, the pro-American conservative Nicolas Sarkozy was asked by Condoleezza Rice what she could do to help him. "Improve your image in the world," he said.

There is a phony realism brandished on the right these days that says no one will ever cooperate with America. Russia and China have their own interests, and any attempt to find common ground is naive. We might as well all hold hands and sing "Kumbaya." Now, of course countries have their own interests, which are often in conflict. But they also often share some interests. A central task of diplomacy is to explore those areas of agreement, build on them and thus create a more stable world. That's why we have treaties on everything from trade to taxation, adhered to by most nations for their collective benefit.

In fact, Obama's approach has already produced remarkable results. Russia and China, after long opposition, agreed last week to a toughening of the nuclear Non-Proliferation Treaty. In a striking shift, Russia signaled that it may support tougher sanctions against Iran. The Obama administration's decision to cultivate a relationship with both countries, to listen to their concerns, is paying off.

Obama's outreach to the world is an experiment, and not merely to see if the world will respond. He wants to demonstrate at home that engagement does not make America weak. For decades, it's been thought deadly for an American politician to be seen as seeking international cooperation. Denouncing, demeaning and insulting other countries was a cheap and easy way to seem strong. In the battle of images, tough and stupid always seemed to win.

Obama is gambling that America is mature enough to understand that machismo is not foreign policy and that grandstanding on the global stage won't succeed. In a new world, with other countries more powerful and confident, America's success -- its security, its prosperity -- depends on working with others. It's a big, bold gambit. I hope it works.

Fareed Zakaria is editor of Newsweek International and the author of "The Post-American World." His e-mail address is comments@fareedzakaria.com.